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A class of extreme lattice-coverings of n–space by spheres

Published online by Cambridge University Press:  09 April 2009

E. S. Barnes  and
D. W. Trenerry
E. S. Barnes
Affiliation:
Mathematics Department, University of AdelaideAustralia
D. W. Trenerry
Affiliation:
Mathematics Department, University of AdelaideAustralia
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All extreme lattice-coverings of n–space by spheres are known for n ≦ 4; see for example [3]. Only one class of extreme covering is known for large n, namely that corresponding to the quadratic form this was first shown to be extreme for all n ≧ 2 by Bleicher [2].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 2 , September 1972 , pp. 247 - 256
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Barnes, E. S. and Dickson, T. J., ‘Extreme coverings of n-space by spheres’, J. Aust. Math. Soc. 7 (1967), 115–127. Corrigendum, 8 (1968), 638–640.CrossRefGoogle Scholar
[2]Bleicher, M. N., ‘Lattice coverings of n-space by spheres’, Can. J. Math. 14 (1962), 632–650.CrossRefGoogle Scholar
[3]Dickson, T. J., ‘The extreme coverings of 4-space by spheres’, J. Aust. Math. Soc. 7 (1967), 490–496.CrossRefGoogle Scholar
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